For anchoring dental prostheses, spheres, crowns or similar anchoring heads are used, which are screwed directly into the implant, which is provided at its upper side with a coaxial connecting borehole with internal thread and are aligned coaxially with the implant. If, for reasons specific to a jaw, the implants for supporting dental prostheses cannot be aligned axially parallel to one another, compensatory measure must be taken and compensatory means used, in order to ensure that the prosthesis is seated satisfactorily and/or handled precisely when put in place and when removed. For this purpose, attachments between all diverging units are used in the case of fixed supraconstructions, whereas, for removable constructions, special secondary crown parts are used which have to be made especially and, after being put in place on their associated primary crowns, must compensate for their divergences. Because of the individual adaptation, such compensatory measures and means are exceptionally labor-intensive and costly and, moreover, represent a burden for the patient because of the frequency of the appointments that are necessary. Furthermore, in the case of attachments, there are always microgaps which permit movements which, from the point of view of a firm support for the implant, are undesirable.